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A picture is worth a
thousand words, so here is a VERY rough animation of what is going on during an
eclipse. You're stationed above the North Pole of the earth, watching the moon's shadow overtake the earth from right to left (West to East).
Notice that an observer stationed on the
spot to the far right only gets totality for a brief time, basically because the
shadow is smaller at that point. For observers farther east along the path, the shadow's bigger
cross-section produces more time in the shadow. This is maximized at a point called
"greatest eclipse", which for the 2017 eclipse occurs near Hopkinsville KY.

(Please note, this is not the point of maximum duration, which occurs in Southern Illinois.)

This
animation is very rough, with an extremely exaggerated scale, and does not
show the effects of the rotation of the earth, which also serves to give
noon-time observers a greater amount of time in the shadow.